for each 10-degree elevation of the tempera- 

 ture, within the range that the organism can 

 tolerate. This high degree of temperature 

 sensitivity is strong evidence that a chemical 

 rather than a purely physical reaction is in- 

 volved, and this is in good agreement with 

 current theory (p. 525). 



GENETIC vs. ENVIRONMENTAL 

 VARIATIONS 



Even among offspring of the same par- 

 entage the interplay of genetic and environ- 

 mental factors results in great variation 

 among organisms — and this accounts for the 

 familiar fact that no two organisms are ever 

 exactly identical. But sharp distinction must 

 be made between environmental variations, 

 which are not perpetuated by the mechan- 

 isms of heredity, and genetic variations, 

 which are so perpetuated. Environmental 

 variations are referred to more technically as 

 modifications; but the importance of modi- 

 fications will be discussed later (Chap. 28). 



The following classification serves to sum- 

 marize and systematize the several kinds of 

 genetic variations that have been mentioned 

 during the discussion on heredity: 



1. Recombinations. Differences among off- 

 spring due to segregation, independent as- 

 sortment, crossing over, random fertilization, 

 and other normal operations of the chromo- 

 somal mechanism. 



2. Aberrations. Variations due to occa- 

 sional irregularities in the behavior of the 

 chromosomes. 



3. Mutations. Transformations by which 

 one gene changes into another. 



Recombination. The numbers of different 

 phenotypes and genotypes produced in sev- 

 eral simple crosses were analyzed previously. 

 These results may be extended and general- 

 ized as follows. Assuming the absence of 

 complete linkage (and this is generally true), 

 any organism that is heterozygous for n pairs 

 of genes will produce 2" genetically different 

 kinds of gametes. Or if one parent is hetero- 

 zygous for m pairs, and the other for n dif- 



Heredity -513 



ferent gene pairs, there will be 2 < "+"' ) differ- 

 ent genotypes among the offspring. Or if 

 both parents are heterozygous for the same n 

 pairs of genes, the number of genotypically 

 different offspring will be 3". If dominance is 

 entirely lacking, the numbers of phenotypes 

 and genotypes will be equal; otherwise the 

 number of phenotypes will be less, although 

 the recessive genes will all appear in subse- 

 quent generations and frequently a recessive 

 gene may have significant "side effects" in 

 each generation. 



In general, therefore, the number of genet- 

 ically different offspring increases more and 

 more rapidly as the parents become hetero- 

 zygous for more and more gene pairs; or in 

 mathematical language, genetic variation in- 

 creases exponentially with heterozygosity. 



Only a small minority of species are self- 

 fertilizing; and a majority of organisms, as a 

 result of random mating, are heterozygous 

 for many genes. Under these conditions, con- 

 sequently, the production of two genetically 

 identical offspring becomes virtually impos- 

 sible, except where more than one individual 

 arises from the same zygote (identical twins, 

 triplets, etc.). In man particularly, owing to 

 random mating and the conservative rate of 

 breeding, genetic identity between any two 

 children lies quite beyond the range of prac- 

 tical possibility. 



Aberration. The processes of mitosis and 

 meiosis are extremely precise and regular, 

 but now and again a slip-up may occur while 

 the countless cells of the species proceed with 

 their divisions. Sometimes a chromosome, or 

 a whole set of chromosomes, may be gained, 

 lost, or misplaced; or just a fragment of a 

 chromosome may experience a similar fate. 

 Moreover, if such an aberration occurs in the 

 cells of the germ cell line, a new and differ- 

 ent complex of chromosomes will automati- 

 cally be transmitted to the offspring; and the 

 changed genetic constitution of the species 

 will be perpetuated. 



The commonest and most important type 

 of aberration involves the gain of one or 

 more whole sets of chromosomes. This may 



